On March 16 Hollywood Reporter shares a riveting interview with "The Walking Dead" star Melissa McBride on what it was like for Carol to kill Lizzie. As fans of the show know, Carol lost her own daughter in the second season and it was a traumatic incident for her. Since then, she's been hell-bent on ensuring that the kids in this season are nurtured to the best of her ability, but sometimes, like in the case of Lizzie, there is nothing that can save them.
McBride says that there was nothing else that could be done than to kill Lizzie. It was clear after she killed her little sister and tried to kill Judith that nobody would be safe with her around. She obviously had sociopathic tendencies before they reached the grove, and it was clear that neither her or Mika had what it took to survive in this post-apocalyptic world.
Because killing Lizzie was inevitable, and sad, Carol learned that everyone has to change. She did what she had to for the greater good. She confessed to Tyreese that she had killed his girlfriend for the same reason and gave him the choice of letting her live or die and he understood that id was likely the best thing for everyone. He allowed her to live and because of that they trust each other 100-percent and can have a fresh new start as they make their way to Terminus.
Carol blames herself for not seeing how damaged the girls were before both of the girls died. It is likely that their mother's death was a traumatic event for both of them. They were very different people, with Mika not being willing to kill anyone, even to save herself, and Lizzie not believing that killing someone matters because they will come back and live forever as a walker. This isn't a world that is safe for anyone and in the end, neither one of them would have survived.
As Mika pointed out to Carol, "Everything works out the way it's supposed to."